[tex] \LARGE{ \boxed{ \mathbb{ \color{purple}{SOLUTION:}}}}[/tex]
We have, Discriminant formula for finding roots:
[tex] \large{ \boxed{ \rm{x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} }}}[/tex]
Here,
x is the root of the equation.a is the coefficient of x^2b is the coefficient of xc is the constant term1) Given,
3x^2 - 2x - 1
Finding the discriminant,
➝ D = b^2 - 4ac
➝ D = (-2)^2 - 4 × 3 × (-1)
➝ D = 4 - (-12)
➝ D = 4 + 12
➝ D = 16
2) Solving by using Bhaskar formula,
❒ p(x) = x^2 + 5x + 6 = 0
[tex] \large{ \rm{ \longrightarrow \: x = \dfrac{ - 5\pm \sqrt{( - 5) {}^{2} - 4 \times 1 \times 6 }} {2 \times 1}}}[/tex]
[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5 \pm \sqrt{25 - 24} }{2 \times 1} }}[/tex]
[tex] \large{ \rm{ \longrightarrow \: x = \dfrac{ - 5 \pm 1}{2} }}[/tex]
So here,
[tex]\large{\boxed{ \rm{ \longrightarrow \: x = - 2 \: or - 3}}}[/tex]
❒ p(x) = x^2 + 2x + 1 = 0
[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm \sqrt{ {2}^{2} - 4 \times 1 \times 1} }{2 \times 1} }}[/tex]
[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm \sqrt{4 - 4} }{2} }}[/tex]
[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm 0}{2} }}[/tex]
So here,
[tex]\large{\boxed{ \rm{ \longrightarrow \: x = - 1 \: or \: - 1}}}[/tex]
❒ p(x) = x^2 - x - 20 = 0
[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{ - ( - 1) \pm \sqrt{( - 1) {}^{2} - 4 \times 1 \times ( - 20) } }{2 \times 1} }}[/tex]
[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{ 1 \pm \sqrt{1 + 80} }{2} }}[/tex]
[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{1 \pm 9}{2} }}[/tex]
So here,
[tex]\large{\boxed{ \rm{ \longrightarrow \: x = 5 \: or \: - 4}}}[/tex]
❒ p(x) = x^2 - 3x - 4 = 0
[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{ - ( - 3) \pm \sqrt{( - 3) {}^{2} - 4 \times 1 \times ( - 4) } }{2 \times 1} }}[/tex]
[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{3 \pm \sqrt{9 + 16} }{2 \times 1} }}[/tex]
[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{3 \pm 5}{2} }}[/tex]
So here,
[tex]\large{\boxed{ \rm{ \longrightarrow \: x = 4 \: or \: - 1}}}[/tex]
━━━━━━━━━━━━━━━━━━━━
Step-by-step explanation:
a)
given: a = 1, b = 5, c = 6
1) Discriminant → ∆= b² − (4*a*c)
∆= b² - (4*a*c)
∆= 5² - (4*1*6)
∆=25 - ( 24 )
∆= 25 - 24
∆= 1
2)
Solve x = (- b ± √Δ ) / 2a
x = ( 5 ± √25 ) / 2*1
x = ( 2 ± 5 ) / 2
x = ( 2 + 5 ) / 2 or x = ( 2 - 5 ) / 2
x = ( 7 ) / 2 or x = ( - 3 ) / 2
x = 3.5 or x = -1.5
b)
given: a = 1, b = 2, c = 1
1) Discriminant → ∆= b² − (4*a*c)
∆= b² - (4*a*c)
∆= 2² - (4*1*1)
∆= 4 - (4)
∆= 4 - 4
∆= 0
2)
Solve x = (- b ± √Δ ) / 2a
x = ( -2 ± √0) / 2*1
x = ( 2 ± 0 ) / 2
x = ( 2 + 0) / 2 or x = ( 2 - 0 ) / 2
x = ( 2 ) / 2 or x = ( 2 ) / 2
x = 1 or x = 1
x = 1 (only one solution)
c)
given: a = 1, b = -1, c = -20
1) Discriminant → ∆= b² − (4*a*c)
∆= b² - (4*a*c)
∆= -1² - (4*1*-20)
∆= 1 - ( -80 )
∆= 1 + 80
∆= 81
2)
Solve x = (- b ± √Δ ) / 2a
x = ( 2 ± √81 ) / 2*1
x = ( 2 ± 9 ) / 2
x = ( 2 + 9 ) / 2 or x = ( 2 - 9 ) / 2
x = ( 11 ) / 2 or x = ( - 7 ) / 2
x = 5.5 or x = -3.5
d)
given: a = 1, b = -3, c = -4
1) Discriminant → ∆= b² − (4*a*c)
∆= b² - (4*a*c)
∆= -3² - (4*1*-4)
∆= 9 - ( -16)
∆= 9 + 16
∆= 25
2)
Solve x = (- b ± √Δ ) / 2a
x = ( 3 ± √25 ) / 2*1
x = ( 3 ± 5 ) / 2
x = ( 3 + 5 ) / 2 or x = ( 3 - 5 ) / 2
x = ( 8 ) / 2 or x = ( - 2 ) / 2
x = 4 or x = -1
Find the area of a parallelogram with a base of 7 metres and a height of 8 metres. Show full working out
Answer:
[tex]56m^2[/tex]
Step-by-step explanation:
Step 1: Area of Parallelogram Formula
A=bxh
Step 2: Plug in the information and solve
A=7mx8m
A=[tex]56m^2[/tex]
Therefore the area of the parallelogram is [tex]56m^2[/tex]
Answer:
56 Meters Squared
Step-by-step explanation:
Area of a Parallelogram is: [tex]A=b*h[/tex]
We are given the base of 7 meters and the height of 8 meters.
[tex]A=7*8\\\\A=\boxed{56}[/tex]
The area of the parallelogram is 56 square meters.
What is the opposite of 100
Answer:
-100
Step-by-step explanation:
The opposite of any positive number is the same number but negative.
Please answer the question below. Please answer
Answer:
I think of (C.85) can't be constructed
Step-by-step explanation:
hope this helps you :)
Answer:
C) 85
Step-by-step explanation:
Hope this helps
Which expressions are equivalent to 3(4h+2k)?
Answer:
(4h+2k)
Step-by-step explanation:
y685
Carlos is using the distributive property to evaluate the expression 14 (49) by using friendlier numbers. His work is shown below. Carlos’s Work 14 (49) Step 1 14 (40 + 9) Step 2 14 (40) + 9 Step 3 560 + 9 Step 4 569 What was the first error that Carlos made?
PLZ HELP ME PLZ PLZ PLZ I NEED HELP
Answer:
The 1st error that Carlos made was in Step 2...
In step 2 , Carlos multiplied 14 only with 40. If he would have multiplied 14 with both 40 & 9 , then it could have been alright.....
Consider triangle GHJ. Triangle G H J is shown. Angle G H J is a right angle. The length of the hypotenuse is 10 and the length of another side is 5. What is the length of line segment HJ?
Answer:
[tex]\bold{\sqrt{75}}[/tex]
Step-by-step explanation:
Given
A [tex]\triangle GHJ[/tex] in which
[tex]\angle GHJ = 90^\circ[/tex]
Hypotenuse = 10
Length of another side = 5
To find:
HJ = ?
Solution:
Kindly refer to the image attached in the answer area.
We know that there are only 3 sides in a triangle.
We are given hypotenuse is 10.
i.e. GJ = 10
To find HJ, Base = ?
So, we are given the side length of GH, perpendicular i.e. 5.
Kindly refer to attached image for further details.
Let us use Pythagorean theorem here.
According to Pythagorean theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow GJ^{2} = GH^{2} + HJ^{2}\\\Rightarrow 10^2=5^2+HJ^2\\\Rightarrow HJ = \sqrt{100-25}\\\Rightarrow \bold{HJ = \sqrt{75}}[/tex]
Answer:
hJ = B 5 route 3
Step-by-step explanation:
got it right on edg 2020-2021
It takes Erin 4 hours to build a statue and Cathy 6 hours to do the same job. How
many hours would it take them to build a statue working together?
Simplify the polynomial a³+a²+ab
Answer:
a (a^2 + a + ab )
Step-by-step explanation:
Step-by-step explanation:
Step 1:
To simplify this polynomial just take the term a as common
a(a^2+a+b)
I need help, please help me
Answer:
1)2A/b=h
2)m1=Fgr'2/Gm2
Step-by-step explanation:
Hope it helps you
Write an equation of the line below.
Answer: y = -2/5x -4
Step-by-step explanation:
First we can notice that the line is not going through the origin but is is going through the y-intercept which is -4.In this case the the equation of the line has be in slope intercept form as if y=mx +b where only m and b is indicated and m is the slope and b is the y intercept. So since we already know the y intercept is -4 we need to find the slope using the points on the line.
The points (0,-4) and ( -5,-2) lies on the line and we could use them to find the slope. To find the slope,we need to find the change in the y coordinates and divide it by the change in the x coordinates.
-4 -(-2) = -2
0 - (-5) = 5
slope: -2/5
So since the slope is -2/5 and the y intercept is -4 then we will have the equation,
y= -2/5x - 4
if the product of two identical number is one thousand twenty four. Find out of the numbers
Answer:
32
Step-by-step explanation:
1,024 will be a perfect square if it is the product of 2 of the same numbers:
Calculate the square root of 1024:
[tex]\sqrt{1024}[/tex]
= 32
So, the number is 32
Answer:
32
Step-by-step explanation:
Let the unknown number be n.
When multiplied together, the product is 1,024. Therefore:
[tex]n\cdot n=1024[/tex]
Combine:
[tex]n^2=1024[/tex]
Take the square root of both side:
[tex]n=\sqrt{1024}=32[/tex]
Therefore, the unknown number is 32.
The level of a pond receded at the rate of 4 centimeters per day. Find the change in the water level of the pond after 7 days.
Answer:
28 centimeters
Step-by-step explanation:
The level of the pond is dropping each day by 4 cm. 7 days passed, and each day it was dropping at a constant rate. In order tto find how many centimeters the level of the pond dropped in 7 days, you have to multiply the days passed by the amount dropped each day.
So, 7 days times 4 cm. a day= 28 centimeters dropped.
Factor the trinomial below.
x2 + 14x + 48
O A. (x+6)(x+8)
B. (x+4)(x+12)
O C. (x-6)(x-8)
O D. (x-4)(x - 12)
Answer:
( x+6)(x+8)
Step-by-step explanation:
x^2 + 14x + 48
What 2 numbers multiply to 48 and add to 14
6*8 = 48
6+8 = 14
( x+6)(x+8)
x² + 14x + 48 [ Given ]
By split middle term ,we get:
=> x² + 8x + 6x + 48
=> x ( x + 8 ) + 6 ( x + 8 )
=> ( x + 6 ) ( x + 8 )
A researcher at a major clinic wishes to estimate the proportion of the adult population of the United States that has sleep deprivation. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 4%?
Answer: n = 600.25 ≈ 601 ( sample size)
the minimum sample size of the adults in United State who have sleep deprivation is 601
Step-by-step explanation:
Given that;
the confidence level = 95% = 0.05
the Margin of error E = 4% = 0.04
∴ level of significance ∝ = 1 - C.L
∝ = 1 - (95/100)
= 0.05
Z∝/2 = 0.05/2 = 0.025
Z-critical value at 95% confidence level is OR level of significance at 0.025 = 1.96 (z-table)
Now to calculate the sample size, we say
n = (Z(critical) / M.E )² P ( 1 - P)
now we substitute
n = (1.96 / 0.04)² × 0.5 ( 1 - 0.5)
n = 2401 × 0.5 × 0.5
n = 600.25 ≈ 601
Therefore the minimum sample size of the adults in United State who have sleep deprivation is 601
Using the formula for the margin of error, it is found that a sample of 601 is needed.
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].
In this problem:
There is no previous estimate, hence [tex]\pi = 0.5[/tex] is used.The minimum sample size is n for which M = 0.04, hence:[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96(0.5)[/tex]
[tex]\sqrt{n} = \frac{1.96(0.5)}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96(0.5)}{0.04}\right)^2[/tex]
[tex]n = 600.25[/tex]
Rounding up, a sample of 601 is needed.
A similar problem is given at https://brainly.com/question/25420216
(-2)+6(-5)+9 find the sum
Answer: We should first use order of operations to multiply 6 and -5. Then we add and subtract from left to right.
Demo:
6 * (-5) = -30
Equation looks like: -2 - 30 + 9
-2 - 30 = -32
-32 + 9 = -23
-23 is the answer to this equation.
What is the midpoint of AB
Answer:
A= (-5, -4)
B = (-3, 3)
x1 = -5 , x2 = -3
y1 = -4 , y2 = 3
[tex]midpoint = ( \frac{x1 + x2}{2} \: \: \frac{y1 + y2}{2} )[/tex]
[tex] = (\frac{ - 5 - 3}{2} \: \: \frac{ - 4 + 3}{2} )[/tex]
= (-4, -0.5)
Does anyone know this?
Answer:
Hey there!
The domain is the range of all the x values.
So for this graph, the domain would be [tex]-10<x\leq 8[/tex].
Note that the open circle means < or > and the closed circle means ≤ or ≥.
Let me know if this helps :)
Solve the equation: 3x - x + 2 = 4(2x - 1) infinite solutions x = 1 x = -1 no solution
Answer:
[tex]x=1[/tex]
B
Step-by-step explanation:
So we have the equation:
[tex]3x-x+2=4(2x-1)[/tex]
Combine like terms on the left:
[tex]3x-x+2=4(2x-1)\\2x+2=4(2x-1)[/tex]
Distribute out the right:
[tex]2x+2=4(2x-1)\\2x+2=8x-4[/tex]
Subtract 2x from both sides. The left side cancels:
[tex](2x+2)-2x=(8x-4)-2x\\2=6x-4[/tex]
Add 4 to both sides. The right side cancels:
[tex]2+4=(6x-4)+4\\6=6x[/tex]
Divide each side by 6:
[tex](6)/6=(6x)/6\\x=1[/tex]
Therefore, the solution is: x=1.
Plz help me I just started 8th grade.
Answer:
I think this is slope. So for each point you go up 3 units. All of the point should connect into a straight line.
Step-by-step explanation:
Mark Point R on the graph to its coordniates. Do the same to Point D, L and F. after you are done then go back to each point and go up 3 units/points. Then draw a line connecting the 4 points. Then you will have your answer. Hope this helped!
What is a “real number “
Please help ASAP please
Answer:
a(sub n)=a(sub n-1)÷4 when n≥2
Step-by-step explanation:
a(sub n)=a(sub n-1)÷4 when n≥2 (the second term)
sorry - my iPad doesn’t let me do subscript. You just have to write an n and n-1 in the lower subscript position after a
sanji has a room with a perimeter of 42.5 feet if she wants to hand a curtain along one full side of the room how long dose the curtain need to be
Answer:
The length of the curtain is 10.625 feet
Step-by-step explanation:
The length of the curtain to cover one side of the room depends on the shape of the room
Given a room shape of a square, we have;
Perimeter = 4 × Side length of the room
Length of the curtain = Side length of the room
Therefore;
Perimeter = 4 × Length of the curtain
42.5 feet = 4 × Length of the curtain
Length of the curtain = (42.5 feet)/4 = 10.625 feet
The length of the curtain = 10.625 feet.
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹27 for a book kept for seven days, while Susy paid ₹21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Answer: fixed charge = 15, extra day = 3
Step-by-step explanation:
Let x represent the charge for an extra day (after 3 days)
Let y represent the fixed charge (for first 3 days)
Equation 1: 7 days is 4 extra days --> 4x + y = 27
Equation 2: 5 days is 2 extra days --> 2x + y = 21
Multiply the second equation by -1 and add the two equations together:
4x + y = 27
-2x - y = -21
2x = 6
x = 3
Input x = 3 into either equation to solve for y:
2x + y = 21
2(3) + y = 21
y = 15
use a number line to determine the new balance of Tims account. What number could be added to the expression 43 + (-52) to result in sum of zero Model your answer using a number line.
Answer:
very urgent by the get together his used handcrafted
Step-by-step explanation:
hand i do like anisajish
Please help assappppp!!!1
Answer:
(D) C'D' and CD are equal in length
Step-by-step explanation:
When we reflect a line, nothing changes about it except it's position.
The line never gets dilated in any way.
This means that B and C must be incorrect, since they refer to dilating the line.
Now we can think about it. If we reflect a line across the y-axis, that means that the line will be parallel to the original line. This means A is false.
That leaves D.
Hope this helped!
i have 18ones,15hundreds,15tens,and 8 thousands
9668
Explanation:
18 ones, 18x1=18
15 hundreds, 15x100 =1500
15 tens, 15x10=150
8 thousands,8x1000=8000
8x1000=800018+1500+150+8000=9668
Hope this answer correct :)
Assume that a, b, and c are real numbers. If a > b, and (a + c) > (b + c), then what is true of c?
Answer:
Problem:
"Assume that a, b, and c are real numbers. If a > b, and (a + c) > (b + c), then what is true of c?"
Answer:
c can be any real number. There is no other conclusion we can come to. This is simply the addition property of inequality.
Answer:
Step-by-step explanation:
c is a real number. We can not know if it is positive or negative
What’s the absolute value for this ?
Answer:
The absolute value for x = 1/6
Step-by-step explanation:
Leave |x + 3| alone
2/3|x + 3| = 11/6 + 1/2 ➡ 2/3|x + 3| = 14/6
|x + 3| = 14/6 ÷ 2/3 ➡ |x + 3| = 7/2 now we write two equations
x + 3 = 7/2 or x + 3 = -7/2 first we subtract 3 from all
x = 1/6 or x = -13/6 since we are asked to find the absolute value, the answer would be 1/6
Evaluate ab – 0.55 when a
1 and b = 5.
HELP PLEASE IM BEGGING SOMEBODY!!??!
Answer:
0.16
Step-by-step explanation:
We can convert 4 / 25 to 16 / 100. Since 100 ends in 2 zeroes, we know that there will be 2 digits after the decimal point, therefore, the answer is 0.16.
Answer:
0.16 is the answer
Step-by-step explanation:
just simply divide 4 by 25 and you ll get the answer